Question
Derive an expression for the position vector of centre of mass of a body consisting of two particles in terms of the their position vectors. Deduce the result for n particles.
Solution
Consider that the body consists of two particles of masses
having position vector 
respectively.
The moment of masses of particles constituting the body about O is, 
Let 
be the position vector of the center of mass.
The moment of mass of center of mass about origin O is, ![<pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
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...(2)
Since moment of mass of the body about any point is equal to the moment of mass of CM about the same point, therefore from equations (1) and (2), we get
For a system of n particles, the position of center of mass is given by, 
